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Japanese have never been quite as fussy about using just one piece of
paper as American and British folders. In one of the most striking branches
of origami, called modular origami, many identical, interlocking units
fit together to form a complex model. (Each of the cubes to the left
is made from twelve identical parts; the different sizes of the cubes
come from the different sizes of the original paper squares.) The units
themselves are not very interesting to fold, but the thrill of modular
origami is assembling the units. The best designs have ingenious systems
of pockets and tabs that lock the whole contraption together without
glue and give it astonishing strength for a paper figure.

Jeremy
Shafer uses a similiar concept of linking with interlocking rings
which he demonstrates in this RealVideo. Shafer's rings, however,
use only one sheet of paper.

Watch
this clip in RealVideo through the link above, or in the following
formats:Quicktime
4.0: 1.5MB or 1MB

Though modular origami dates
back hundreds of years, a folder named Mitsunobu Sonobe invented the
locking mechanism that has made it popular. Variants of his unit, as
well as completely new designs, are being invented all the time.

obert Lang, a laser physicist
from Pleasanton, California, has moved origami into the electronic age.
A computer program he has written, called TreeMaker, can take any stick
figure and calculate a pattern of creases that will produce that figure.
For example, to create the lobster below, Lang drew a stick version
to determine how many appendages it needed, how they connected, and
how long they should be. Then he gave the information to TreeMaker,
which printed out this folding pattern (left).

The
lobster (shown below) is a complex creature that was designed
by Robert Lang using TreeMaker, the software he developed.

If you fold along the lines
the right way, you get a primitive lobster model with flaps of paper
that correspond to each limb of the stick figure. From there, Lang says,
he uses his origami experience - not the computer—to transform
the flaps into claws that look as if they might pinch you if you get
too close. "After a while, you learn the repertoire of how you
put in elbows or feet," Lang says. "The hard part is getting
the flaps in the right places to begin with."

The secret of TreeMaker lies
in the circles that have been drawn on the crease pattern. Each circle
corresponds to one appendage. For example, the gigantic circle eventually
turns into the lobster's tail. Inside each circle, the creases fan outward
like the spokes of an umbrella. When collapsed, each of these "umbrellas"
becomes a narrow, straight projection or flap, which Lang subsequently
shapes into the appendage of choice. The computer packs the circles
together as tightly as possible (to avoid wasting paper), while respecting
the overall geometry of the lobster.

This type of mathematical
problem is called "constrained optimization"—finding
the optimum design that satisfies certain constraints, such as the proportionality
of the lobster's limbs. It's also exactly the type of problem Lang solves
in his day job as a designer of laser systems. "Is it just lucky
coincidence," Lang asks, "or is it that to a man with a hammer,
everything looks like a nail?"